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Semigroups corresponding to algebroid branches in the plane

Author: H. Bresinsky
Journal: Proc. Amer. Math. Soc. 32 (1972), 381-384
MSC: Primary 14J15
MathSciNet review: 0291171
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Abstract: The symmetric semigroups of nonnegative integers and their generators, corresponding to algebroid branches of the plane, are determined.

References [Enhancements On Off] (What's this?)

  • [1] R. Apéry, Sur les branches superlinéaires des courbes algébriques, C. R. Acad. Sci. Paris 222 (1946), 1198-1200. MR 8, 221. MR 0017942 (8:221a)
  • [2] M. A. Hoskin, Zero-dimensional valuation ideals associated with plane curve branches, Proc. London Math. Soc. (3) 6 (1956), 70-99. MR 17, 665. MR 0074905 (17:665b)
  • [3] J. G. Semple and G. T. Kneebone, Algebraic curves, Oxford Univ. Press, London, 1959. MR 23 #A2111. MR 0124801 (23:A2111)

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Keywords: Algebroid branch of a plane curve, semigroup of a branch, infinitely near points, multiplicity sequence, multiplicity matrix, proximity structure, satellite cluster, free point, restriction, leading point
Article copyright: © Copyright 1972 American Mathematical Society

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